Tag Archives: Leibniz

It’s also Canada’s 150th birthday, but Leibniz day takes precedence for me. The guy invented calculus, yo. Would Canada even exist without calculus?

I GUESS WE’LL NEVER KNOW, WILL WE

(Sorry, I’m hyper.)

I also did a 30-mile walk this afternoon/evening. It took me 6 hours and 18 minutes, but I kept a pace of 4.77 MPH despite it being obscenely hot and then obscenely thunderstormy. My feet/legs didn’t feel any worse than they do after a typical 15-mile walk, so hey, that’s cool. I’mma try it again on Monday.

Today I had to go invigilate a MATH 277 final as part of my TA requirements (we each have to invigilate/proctor two final exams; sometimes we get ones we’ve actually been TAs for and sometimes we don’t. This was a case of the latter). It turns out that MATT 277 is University of Calgary’s version of MATH 275, or multivariate calculus. The test involved about 20 or so questions.

Our job as TAs, apart from making everybody sign in on the little attendance sheet, was mainly to just walk around in order to discourage cheating and to help anybody out who raised their hand.

So let me just quickly set the scene for you: a large gym full of 250+ students, a 2-hour exam, and lots and lots of calculus.

I bet you can guess what I was thinking about.

I was thinking about Leibniz!

I was wondering, as I walked down the aisles of seats, watching students write the elongated “s” for integration and the dx/dy (or variations of that) for differentiation, what Leibniz would think if he saw a roomful of people, in 2016, still using some of his original symbols. Like, how ridiculous is that? Calculus has been studied, expanded upon, and extended to a ton of different fields/uses since it was first developed, but we’re still using some of Leibniz’ original symbols.

And what would he think about calculus being taught as basically standard curriculum at universities? What would he think about the tons of different uses of calculus today?

I know I kind of talked about this in a previous post, but I actually think about this quite a bit. Especially today.

Man, I’d get a study group together right away. And by “study group” I mean “just Leibniz and me, somewhere quiet where he can do his genius stuff and I can guard him ‘cause he’s precious.”

I can’t help it, I’m obsessive. Seriously, if I was ever given the option to, say, time travel back to any year (and location) of my choice, I would with zero hesitation pick something involving Leibniz.

On occasion (read: every day), I find myself wondering what Leibniz would think of our modern world nowadays. Like, if we were somehow to manage to bring him back to life at age 40 or so and got someone (read: me) to show him around and calm him down when all the new stuff freaked him out, I wonder what he would really think of things.

What would he think of modern calculators? His Stepped Reckoner weighed like 80 pounds and could only add, subtract, multiply, and divide. I can buy a palm-sized calculator from the dollar store that can compute any given square root in about the time it takes to blink. And what would he do with a graphing calculator?

On the larger scale, what would he think of computers? He may have not come up with the original idea for binary, but he certainly refined it enough so that it could be easy to understand and use. Would he be surprised at how far we’ve come technology-wise just based on binary, or would that be something he may have anticipated?

And what would he think about technology in general? Like, I’m sure if we just recreated 40-year-old Leibniz and dropped him into the modern world, he’d likely be VERY freaked out, but barring that—say we were able to calm him down and explain things to him—what would he think of our technology now? I’d bet he’d want to deconstruct EVERYTHING to see how it all works, and it wouldn’t surprise me if he just came up with a few improvements off the top of his head. ‘Cause, you know, Leibniz.

How would he feel about the fact that now, in 2015, we still use several of his original symbols in calculus? If I were to show him a college calculus textbook, flip to the first section on integration, and point to his elongated “s” symbol, what would his reaction be? Would he think the textbook was from some previous century? Would he realize that the time he spent thoughtfully considering appropriate and intuitive symbols to describe math was not wasted? I wonder if he’d approve or disapprove of the modern calculus textbook in general.

WHAT WOULD HE THINK ABOUT GLASSES? The poor guy was ridiculously near-sighted by the time he was about 20. Reading and writing must have been quite difficult for him. A good pair of specs would allow him to see clearly, both near and far. I wonder what his reaction to that would be.

What would he think about his Wikipedia page, or any other brief history of his life/accomplishments? Would he feel proud seeing the long list of accomplishments that he’d achieved during his life? Would he wish he’d had more time to do more things? (Probably.) I wonder if he’d be happy with how people see him nowadays and/or how they interpret his philosophical contributions and his general view of the world.

Interesting things to think about. I also like the idea of him impulsively shunning the fashion of his day in favor of some outfit he saw at H&M or something. He’d go running through the store towards it, shedding clothes and knocking over all the displays along the way.

You know what the only downside is to LeibnizFest?* Reading the last chapter of that Antognazza biography.

Man, is it sad.

Leibniz did not have a very good time at the end of his life. “Leibniz’s last years were marred by frustration and loneliness,” is the first sentence of that last chapter, and unfortunately it is a very fitting first sentence. First, he’d outlived almost everyone he’d ever communicated with (most of them died in the 1690’s; Leibniz lived until 1716) and thus had very few people to communicate with. Second, he was still trying to recover his reputation after the whole calculus debate with Newton (and actually, I shouldn’t say “after” yet because Newton and his cronies (mostly his cronies) dragged that thing out well past Leibniz’ death). Third, he wanted desperately to keep traveling, but injury, poor health, and prior obligations basically forced him to stay put for a good several years. A quote of his from the bio: “I am shut in my room working and I hardly ever leave it.” This is coming from a man who took on innumerable projects just so that he’d have the excuse to travel and converse with people of different backgrounds and skills, so it’s super sad. And then, of course, there’s the fact that he basically died alone and was given very little recognition for his accomplishments until well after his death.

It’s heartbreaking to me to hear all the crappy things that happened to him in the last five or so years of his life. Someone with such a great mind, such compassion, and such good spirit deserved something better at the end.

UGH IT JUST MAKES ME UPSET, OKAY?

To end LeibnizFest on a lighter note, have a look at this Leibniz-centric website that has pretty much everything you could ever want on the amazing polymath. I have it bookmarked. I visit it a few times a week.

Hint 1: He was a Swiss mathematician born in 1667
Hint 2: He tutored l’Hopital in mathematics
Hint 3: Most of his family members were mathematicians as well

Give up?

It’s JOHANN BERNOULLI!

So why is he awesome?

Not only did he tutor l’Hopital—which eventually led to l’Hopital publishing the first formal book on calculus**–but he also tutored Euler when Euler was young. In fact, he was the one who convinced Euler’s father that he had the makings of a great mathematician, thus steering him away from a life of a pastor.

For a majority of his life, he was in a highly competitive relationship with his equally mathematically talented brother, Jakob. When his brother died of tuberculosis, Bernoulli’s jealousy actually shifted to his son (another mathematician!) and they had a few good disputes about who came up with what papers and ideas.

One super awesome thing about Bernoulli, though, was that he was one of the few who stayed on Leibniz’ side of the whole calculus dispute with Newton. He showed his support by demonstrating several problems that could be solved using Leibniz’ methods, but not Newton’s. Go Bernoulli!

Yay.

*He was born on July 27th by old style dates; by new style, he was born on August 6th.**The book was basically all of Bernoulli’s teachings written up formally, which ticked Bernoulli off quite a bit even though l’Hopital mentioned him in the book.

As I mentioned a week or so ago, I’m re-reading this fantastic bio of him ‘cause it’s important. I know I do this a lot, but let me reiterate just one huge reason why this man is so damn awesome, since it IS his birthday, after all:

Leibniz’ formal schooling was severely lacking any rigorous mathematical training. It focused mainly on Latin, theology, and philosophy. However, due to (among other things) having access to his father’s extensive library, Leibniz developed a curiosity toward mathematics and taught himself quite a bit. However, he was still lacking a lot of knowledge once he got out of school. Here’s an excerpt from the bio regarding his visit to Paris, which was practically the center of all things intellectual in the European continent at the time:

“[In Paris] Leibniz was made painfully aware of the limitations of his mathematical preparation and of his lack of up-to-date knowledge of work in the field; and this soon led to the further realization that, in order to carry his plans forward, he would first need to forge himself new tools. … Thankfully, Leibniz was nothing if not a quick learner: by the end of his Parisian sojourn, in fact, the self-confessed mathematical apprentice had invented the infinitesimal calculus.”

So it took him approximately TEN FREAKING YEARS to go from practically a math novice to inventor of calculus.

If you know anything about me at all, you know that I love Leibniz. What better way to pay tribute to him in tattoo form than to get a tattoo of his symbol for integration? So it works on the level of Leibniz tribute.

It also works on the level of my liking stats—after all, integration is used quite a bit in many statistical applications/techniques. And since that is the case, it saves me from having to pick a specific statistical formula or expression (which I could never do; I love them all!).

I also just really like this symbol. I thought it was very elegant even before I knew that Leibniz came up with it.

It really does have a lot more meaning to me than I can express here, but I tried, haha. I think I’m going to try and plan it so that I get it done (or mostly done) on July 1st this summer.

“In The New Science, you play the role of one of the great scientists from the scientific revolution in 17th century Europe. You are attempting to publish your remarkable scientific discoveries in order to gain prestige, be seen as the finest mind of your era, and consequently be appointed the first President of the Royal Society.”

I submit that on Wikipedia, you can get from the page of any mathematician to Leibniz’ page in 6 clicks or less (even without clicking through the “Mathematician” or “Mathematics” links that show up in like the first sentence of every mathematician’s Wiki page).